When transmitting a modulated optical signal in an optical fiber link, the wavelength dependence of the effective index of the fiber fundamental mode induces differences in the propagation delays experienced by the various spectral components. For a narrowband signal at a given wavelength, the propagation delay is called group delay (GD) and is typically expressed in ps. The GD is calculated with equation (1) where λ is the wavelength, φ is the optical phase and c is the speed of light.
                    GD        =                                            -                              λ                2                                                    2              ⁢              π              ⁢                                                          ⁢              c                                ⁢                                    ⅆ                              ϕ                ⁡                                  (                  λ                  )                                                                    ⅆ              λ                                                          (        1        )            
For example, the optical phase in (1) can be modified by an optical filter or by propagation through an optical fiber. The spectral variation of the GD is called chromatic dispersion (CD). The CD is the slope of the GD curve with respect to wavelength and is expressed in ps/nm.
In the presence of CD, an optical signal is distorted and inter-symbol interference can appear at the output of a long fiber link. This problem is usually addressed by the use of CD compensators which introduce a CD with an opposite value (negative vs positive) to that induced by a given optical fiber length. A standard G.652 optical fiber has a CD value around 17 ps/nm-km. Optical networks with Wavelength Division Multiplexing (WDM) transmit several optical channels spaced by 50 GHz, 100 GHz or 200 GHz over a predetermined optical band. For example, the C-band covers the wavelength range between 1530 nm and 1570 nm. One difficulty in CD compensation is that the CD is not constant between 1530 nm and 1570 nm and, furthermore, this variation depends on the fiber type. This wavelength dependence is called the CD slope (CDS) and is expressed in ps/nm2. Wideband multi-wavelength CD compensators have to take this difference into account because CDS has a critical impact on the performance of high bit rate data link.
In optical networks, the CD can vary as a result of reconfigurations of the network or variations in the environment, for example temperature. Tunable CD compensators are therefore needed to dynamically adjust the CD compensation level over a given range. Furthermore, to have more adaptability, tunable CD compensators must be able to compensate the CDS. Desired properties of a tunable CD compensator therefore include flexibility on the setting of the mean CD value across the whole spectral band, called nominal value, and on the setting of the CDS. Ideally, tunable CD compensators should provide independent CD setting for each optical channel. This feature is particularly important when the channels present in the covered spectral band are propagated through different link lengths.
Fiber Bragg Grating Dispersion Compensator
Fiber Bragg gratings (FBGs) consists of a refractive index modulation along the fiber axis, denoted z. The resulting effective index modulation is expressed by (2).
                                          n            eff                    ⁡                      (            z            )                          =                                            n              ave                        ⁡                          (              z              )                                +                      Δ            ⁢                                                  ⁢                          n              ⁡                              (                z                )                                      ⁢                          sin              ⁡                              (                                                      ∫                    0                    z                                    ⁢                                                                                    2                        ⁢                        π                                                                                              Λ                          G                                                ⁡                                                  (                                                      z                            ′                                                    )                                                                                      ⁢                                                                                  ⁢                                          ⅆ                                              z                        ′                                                                                            )                                                                        (        2        )            Where neff is the effective index of the optical fiber, nave is the average effective index, Δn is the effective index modulation and ΛG(z) is the local grating period. FBGs reflect the incoming light which has spectral components close to the Bragg wavelength (λB) expressed in (3).λB(z)=2naveΛG(z)  (3)
Chirped FBGs (CFBGs) are FBGs in which ΛG varies along the fiber propagation axis. According to (3), the wavelength of the reflected signal, λB, will also vary along the optical fiber axis. This longitudinal λB variation introduces a propagation delay between the different spectral components of an incoming signal. The delay is related to the position along the fiber axis at which the reflection is maximized for the respective wavelengths. A single channel CD compensator may thus be realized by using a small linear variation of ΛG(z) as is schematically represented in FIG. 1A (PRIOR ART). Longer wavelengths of the reflected spectral band (λL) are reflected into the first part of the CFBG, which have shorter propagation delay, while central wavelengths (λC) and shorter wavelengths (λS) are reflected afterwards. For a fixed reflection bandwidth, the CD value of a CFBG is related to its chirp. FIG. 1B (PRIOR ART) illustrates a single channel CD compensator with a higher CD, with smaller chirp, than (a) for the same reflection bandwidth.
Single channel tunable CD compensators can be obtained by inducing a longitudinal variation of neff or ΛG which changes the reflection position of each wavelength along the CFBG. Different implementations of this technique are disclosed in U.S. Pat. No. 5,671,307 (Lauzon et al.) using a temperature gradient, in U.S. Pat. No. 5,964,501 (Alavie) and U.S. Pat. No. 6,360,042 (Long) with a strain gradient or with magnetostriction in U.S. Pat. No. 6,122,421 (Adams et al.).
Multi-wavelength FBG CD compensators can be obtained by superimposing many CFBGs with spectral responses centered at different wavelengths spaced by 50 GHz, 100 GHz or 200 GHz (Y. Painchaud, H. Chotard, A. Mailloux, Y. Vasseur, “Superposition of chirped fibre Bragg grating for third-order dispersion compensation over 32 WDM channels”, Electronics Letters vol. 38, no. 24, pp. 1572-1573 (2002)), or by using FBGs sampled in amplitude and phase (H. Li, Y. Sheng, Y. Li, and J. E. Rothenberg, “Phased-Only Sampled Fiber Bragg Gratings for High-Channel-Count Chromatic Dispersion Compensation”, J. Lightwave Technol vol. 21, pp. 2074-2083 September 2003). In these devices, compensation of CDS is possible with proper control of the FBG characteristics. This is schematically demonstrated in FIGS. 2A and 2B (PRIOR ART) where a three channel CD compensator is illustrated with a CD that has an inter channel variation to compensate the CDS of an optical fiber link. Similarly to single CFBG, CD tunability is achieved by applying a longitudinal perturbation along the FBG. However, these devices do not offer independence of the average CD setting of each channel and therefore do not provide CDS tunability. To overcome this limitation, the use of a cascade of two multi-wavelength CD compensators is disclosed in Canadian patent application no. 2,417,317 (Morin et al.).
CD Compensators with Distributed Resonant Cavities: Principle of Operation
Resonant Cavity Basis
Two parallel and highly reflective mirrors form a resonant optical cavity in which constructive interference occurs for specific cavity modes. The frequency spacing between each cavity mode is called the Free Spectral Range (FSR) and is obtained with (4), where c is speed of light in vacuum, d the distance between the mirrors and ng is the group index of the medium between the mirrors, ng=neff−λ(dneff/dλ).
                    FSR        =                  c                      2            ⁢                          n              g                        ⁢            d                                              (        4        )            
The spectral position of each cavity mode is evaluated with (5), where λm, the mth cavity mode, is directly related to the average of the effective refractive index of the medium.
                              λ          m                =                              2            ⁢                          n              ave                        ⁢            d                    m                                    (        5        )            FBG-Based Resonant Cavities
Resonant cavities need at least two mirrors which are spatially separated. An all-fiber wideband resonant cavity can be formed by two CFBGs, with the same reflection band, that are partially superimposed with a small longitudinal shift (d) along the fiber axis. In S. Doucet, R. Slavik, Sophie LaRochelle. “High-finesse large Band Fabry-Perot fibre filter with superimposed chirped Bragg Gratings”, Elec. Lett., Vol. 38, no 9, April 2002, pp. 160-160, a Fabry-Perot interferometer with two mirrors of similar reflectivity, was realized with superimposed CFBGs. Another type of interferometer is formed with one strong back mirror and other weaker mirror on the input side. This interferometer is an asymmetric Fabry-Perot, which is called a Gires-Tournois etalon (GTE). GTEs are used in reflection to modify the phase and to induce dispersion on an incident optical signal. Indeed, due to their strong back reflectors, GTEs are constant amplitude filters called all-pass filters. However, at the wavelengths corresponding to the cavity modes, the filter will introduce an important GD on the reflected signal. This GD is created by the resonance of the optical field inside the structure which results in a periodic GD response in the spectral band of the mirrors. By carefully designing the reflectivity and position of the weaker mirror, GTEs allow the shaping of the GD variations close to the λm. Similarly to Fabry-Perots, GTEs are realized by superimposed CFBGs. Due to the distributed nature of the CFBGs, this type of GTE is called a distributed Gires-Tournois etalon (DGTE). FIGS. 3A to 3C (PRIOR ART) schematically illustrate the characteristics of a DGTE. In FIG. 3A, two CFBGs with different modulation strengths are shown, photo-induced in an optical fiber but spatially shifted by d along the fiber axis. FIG. 3B represents the relationship between the position along the fiber axis and the local Bragg wavelength, or maximum reflected spectral component of each CFBGs. FIG. 3B also illustrates the resonating cavity mode (λm, λm+1, λm+2) as well as wavelengths that are not resonating (λam, λam+1). In FIG. 3C, the GD response of a typical DGTE is illustrated. It is shown that the GD response follows a monotonous slope, induced by the chirp of the CFBGs, on which GD delay peaks appear around wavelengths corresponding to the resonant cavity modes.
Principle of CD Compensator Based on GTE Cascade
The periodic GD response of DGTEs as explained above may advantageously be used to build devices for CD compensation. In the simplest example of such a device, a single DGTE can act as a simple CD compensator when the channel bandwidth is much smaller than the FSR of the DGTE element. However, this solution is not viable for high bit rate data transmission such as 10 Gbit/s, 40 Gbit/s or higher.
Another possibility is to use two GTE or DGTE components in a cascade configuration, with the two components (a) and (b) having opposite chromatic dispersion slope over the channel bandwidth. FIGS. 4A to 4F (PRIOR ART) illustrate the tunability principle. The upper graphs (FIGS. 4A to 4C) show the CD of the individual components and of the cascade, while the lower graphs (FIGS. 4D to 4F) display their respective GD. The GD characteristic of component (a) shows a quadratic dependence on wavelength detuning over a spectral region larger than the channel bandwidth, but smaller than one FSR, while component (b) covers the channel bandwidth. Their cascade results in an almost linear GD as is represented by the dash-dot line which in turn corresponds to a constant CD over the channel bandwidth. As can be seen by comparing the graphs from left to right, a shift of the spectral response of component (a) results in different CD setting over the channel bandwidth. A tunable multi-channel CD compensator can thus be realized because the DGTE can be made with periodic spectral responses with a FSR of 50 GHz, 100 GHz, 200 GHz or any desired channel spacing.
Actual Chromatic Dispersion Compensators Based on the GTE and DGTE Cascade Principle
CD dispersion compensation was demonstrated with GTE filters, fabricated with thin film technology, and DGTE filters implemented with CFBGs. The latter case is for example shown in X. Shu, K. Sugden, P. Rhead, J. Mitchell, I. Felmeri, G. Lloyd, K. Byron, Z. Huang, Igor Khrushchev and I. Bennion, “Tunable Dispersion Compensator Based on Distributed Gires-Tournois Etalons,” IEEE Photon. Technol. Lett. vol. 15, pp. 1111-1113, August 2003. Published patent application US2003/0210864 (Sugden at al.) also teaches of various DGTE-based devices for CD compensation. However, the proposed DGTE are limited in dispersion range and channel bandwidth.
In X. Shu, Karen Chisholm, and Kate Sugden, “Design and Realization of Dispersion Slope Compensator Using Distributed Gires-Tournois Etalons,” IEEE Photon. Technol. Lett. vol. 16, pp. 1092-1094, April 2004, it is clearly demonstrated that CDS compensation is possible when the DGTEs have different values of FSR. However, the CDS is determined by the design and cannot be tuned, although tuning of the nominal CD, which affects the CD of all channels in similar way, remains possible. FIG. 5A (PRIOR ART) shows the CDS of different FSR mismatch while FIG. 5B (PRIOR ART) shows the tuning of the device to different CD settings. It is evident from FIG. 5B that, although the nominal CD value changes, the inter-channel CDS, corresponding to the CD difference between the channels, remains constant.
In X. Shu, J. Mitchell, A. Gillooly, K. Chisholm, K. Sugden and I. Bennion, “Tunable dispersion Slope compensator using novel tailored Gires-Tournois etalons,” in Optical Fiber Communication on CD-ROM (The Optical Society of America, Washington, D.C., 2004), WK5, the CDS tunability is obtained by using DGTE with CFBGs with tailored reflectivity profiles along the fibers axis. This solution does not offer independent tunability of the CDS and of the nominal CD. Furthermore, some channels have a limited dispersion range, as can be observed in FIG. 6 (PRIOR ART) for the channels with the shorter wavelengths.
In D. J. Moss, M. Lamont, S. McLaugthlin, G. Randall, P. Colbourne, S. Kiran and C. A. Hulse, “Tunable Dispersion and Dispersion Slope Compensators for 10 Gb/s Using All-Pass Multicavity Etalons,” IEEE Photon. Technol. Lett. vol. 15, pp. 730-732, May 2003, thin film multi-cavity GTEs allow compensation over a larger CD range. CDS compensation using two GTEs with different FSR has also been demonstrated with this technology. Thin film GTEs have the same limitations as the previously described DGTE design and cannot allow complete inter-channel tunable CD compensator.
Despite all of the technological advancements described above, there is still a need for a versatile device which would allow for the channel per-channel compensation of CD and CDS.